A121997 Count up to n, n times.

1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7

Offset

1,3

Comments

The n-th block consists of n subblocks, each of which counts from 1 to n.

This a fractal sequence: removing the first instance of each value leaves the original sequence.

The first comment implies that this gives the column index of the n-th element of a sequence whose terms are coefficients, read by rows, of a sequence of matrices of size 1 X 1, 2 X 2, 3 X 3, etc.; cf. example. The row index is given by A238013(n), and the size of the matrix by A074279(n). - M. F. Hasler, Feb 16 2014

Links

Table of n, a(n) for n=1..105.

Example

Sequence begins:
  1;
  1,2;
  1,2;
  1,2,3;
  1,2,3;
  1,2,3;
  ...
The blocks of n subblocks of n terms (n=1,2,3,...) can be cast into a square matrices of order n; then the terms are equal to the index of the column they fall into.

Prog

(PARI) A121997(N=9)=concat(vector(N, i, concat(vector(i, j, vector(i, k, k))))) \\ Note: this creates a vector; use A121997()[n] to get the n-th term. - M. F. Hasler, Feb 16 2014
(Python)
from sympy import integer_nthroot
def A121997(n): return 1+(n-(k:=(m:=integer_nthroot(3*n, 3)[0])+(6*n>m*(m+1)*((m<<1)+1)))*(k-1)*((k<<1)-1)//6-1)%k # Chai Wah Wu, Nov 04 2024

Crossrefs

Cf. A081489 (locations of new values), A075349 (locations of 1's).

Cf. A000290 (row lengths), A002411 (row sums), A036740 (row products).

Cf. A002024 and references there, esp. in PROG section.

Cf. A238013.

Sequence in context: A248141 A220694 A136314 * A023128 A237260 A249727

Adjacent sequences: A121994 A121995 A121996 * A121998 A121999 A122000

Keyword

easy,nonn,tabf

Author

Franklin T. Adams-Watters, Sep 11 2006

Status

approved